Quadratic polynomials in glm and confidence interval of extremum
It is frequent that a variable is modeled using quadratic equation in glm if we suspect that there is a minimum or maximum. However it is less easy to characterize where is located the extremum. One solution is given here but it does not allow to direct fit the data: Stimson JA, Carmines EG, Zeller RA (1978) Interpreting polynomial regression. Sociological Methods & Research 6 (4):515-615 Let do an example: First generate some data: xobs <- 1:100 # If a2 positive, the parabole has a minimum # If a2 negative, the parabole has a maximum # The value of a2 is related to the curvature at the point x=b a2 <- 0.1 # The b value is the position of the maximum or minimum b <- 40 # The c value is a shift parameter. The "0" will be at c ! c <- 100 yobs <- a2*(xobs-b)^2+c plot(xobs, yobs, ylim=c(0, 400), type="l", bty="n", las=1) This second order equation is not of the classical form a2*x^2+a1*x+a0 and thus it